Random booklist
loom91 said:
Privetisation of education is a highly charged political issue here.
As here, where a fairly new phenomenon is privatised primary education. That is, in cases where particular "school districts" (city government level (dis?)-organizations which run local public schools) have done particularly badly on standardized nationwide reading/math exams, the local schools are now sometimes taken over by private companies. The question of how well this works is a political "hot potato" in the U.S.
loom91 said:
Remember that the greatest brains in India attempt this examination. One of the questions involved refraction through an inhomogenous optical media (we are not supposed to know Fermat's principle).
So its a cross between an entrance exam and a national talent exam? (In the U.S., at the high school level there are entrance exams for elite "magnet schools", and at the undergraduate level in mathematics there is a talent search, the Putnam exam.)
loom91 said:
I haven't heard any of this before. Corruption is indeed widespread, though I can't compare with other countries. Plagarism is also common. Recently the doctorate of a researcher was revoked because his thesis was found to contain a large amount of content copied verbatim from a textbook, including errors.
Interesting. Do you happen to have a link to a newspaper article in English or something like that?
Check out http://arxiv.org/new/withdrawals.aug.07.html for a huge scandal at the arXiv, in which two distinct plagiarism rings (both operating in Turkey, as it happens) were recently uncovered when a facutly member at one of the institutions became suspicious about the output of 40 papers over two years by two graduate students
loom91 said:
So, any suggestions about those math books?
Didn't you say your budget has already been exhausted? FWIW, the suggestions I saw above seemed pretty good ones. I'd probably give greater weight to books which discuss great ideas but which I think have a better chance of being useful to someone who dips into or skims rather than studying very carefully over many months, and the greatest weight of all to books which should reward all three styles of reading. And I'd limit my suggestions to textbooks discussing the very best of modern mathematics. On this basis, some books which happened to pop into my mind are:
Some Great Books notable for their charming style as well as their delightful content:
E. Atlee Jacson,
Perspectives of Nonlinear Dynamics, two volumes, University of Cambridge Press, 1991.
Bela Bollobas,
Modern Graph Theory, Springer, 1998.
Tristan Needham,
Visual Complex Analysis, University of Cambridge Press, 1998.
Hilbert and Cohn-Vossen,
Geometry and the Imagination, Chelsea, 1990 (translation of 1932 classic).
Rademacher and Toeplitz,
The Enjoyment of Mathematics, Princeton University Press, 1957.
Ulam and Kac,
Mathematics and Logic, Praeger, 1968.
Cox, Little, and O'Shea,
Ideals, Varieties, and Algorithms, Springer, 1992.
Hardy and Wright,
An Introduction to the Theory of Numbers, 5th edition, Oxford University Press, 1979.
Arnold,
Ordinary Differential Equations, Springer, 1992.
Halmos,
Finite Dimensional Vector Spaces, Van Nostrand, 1958.
Kac,
Statistical independence in probability, analysis and number theory, Wiley, 1959.
Some Really Good Math Books of Which I Happen to Be Particularly Fond:
Harris,
Algebraic Geometry, Springer, 1992.
Gibson,
Elementary Geometry of Algebraic Curves, Cambridge University Press, 1998.
Michael Artin,
Algebra, Prentice Hall, 1991.
Khinchin,
Continued Fractions, Dover 1994 (reprint of translation of 1949 original)
Cover and Thomas,
Elements of Information Theory, Wiley, 1981.
Kapur and Kesevan,
Entropy Optimization Principles with Applications, Academic Press, 1992.
Lawvere and Schanuel,
Conceptual Mathematics, Cambridge University Press, 1991.
Flanders,
Differential Forms with Applications to the Physical Sciences, Dover, 1989 (reprint of 1963 original).
Guenther and Lee,
Partial Differential Equations of Mathematical Physics and Integral Equations, Dover, 1996 (reprint of of 1988 original)
Olver,
Applications of Lie Groups to Differential Equations, 2nd edition, Springer, 2000.
Boas,
A Primer of Real Functions, Wiley, 1960.
Bartle,
Elements of Real Analysis, Wiley, 1964.
Neumann, Stoy, and Thomspon,
Groups and Geometry, Oxford University Press, 1999.
Lee,
Introduction to Smooth Manifolds, Springer, 2003.
Hatcher,
Algebraic Topology, Cambridge University Press, 2002.
I would also suggest some volumes from the "LMS student text series", e.g. 5, 32, 35, 40, 45, 50, 53, 58. Also, the Chauvenet Prize papers (two volumes) from the American Mathematical Association.
Alright, I could add more, that's enough.
I stress that I didn't try to cover topics, just to name some books which I think might have a wide appeal and might reward more than one type of reader or style of reading. The kicker is that this library would have "prerequisite gaps" to which I haven't paid any heed but which your reading club would have to deal with.
and I don't think that was the reason for the communication problem.